Travel

Click here for travel directions. The School of Mathematics is at 21-23 Senghennydd Road and is 200m from Cathays railway station. It takes 20-25 minutes to walk to the School from Cardiff Central railway station.

We refer to the theory of functional models first developed by Sz.-Nagy and Foias in the 1950's and 60's to classify contractive operators and successfully generalised to tuples of operators by Popescu in the 1990's. In a different direction we found a generalisation where a larger class of analytic functions can be used to classify certain contractive liftings of contractive operators or operator tuples. By lifting we mean here: going from an operator C to an operator on a larger space which is a lower triangular 2x2-operator matrix with C in its upper left corner. This is joint work with S. Dey from Mumbai. We intend to explain the basic ideas of this approach and to report on recent progress.

We present some recent results on the variational analysis of some classes of quasilinear elliptic boundary value problems. In particular we show how to characterize the possible lack of compactness due to critical growth of the nonlinearities involved, in order to prove the existence of solutions.

The report is devoted to the survey of recent results in the area of Wiener-Hopf factorization (or, simply, factorization) of matrix functions. Such factorization means representation of a matrix function given on a closed
curve on the complex plane in form of the product of three items (first, analytically continued into the inner domain, third, analytically continued into the outer domain, and the middle term being a diagonal matrix with
power-type monomials). Preliminary information on the subject will be given. Main attention will be paid to constructive methods. The range of known application will be described.

From simple particle models to PDE dynamics - Johannes Zimmer (Bath)

One often aims to describe systems out of equilibrium by the governing energy E and entropy S, as well as the corresponding evolution laws for E and S. How can we derive these ingredients of the macroscopic evolution from particle models? In recent years, a dynamic scale-bridging approach has been developed and applied to a number of problems; large deviation theory plays an important role. The talk will present some of these results, in particular discuss the Vlasov-Fokker-Planck equation as a system driven by energy and entropy. Time permitting, an approach of deriving stochastic equations mimicking the fluctuations in underlying mesoscopic models will be sketched.